Tire/wheel assemblies can produce annoying vibration in the vehicles on which they are used. Complaints concerning such vibration are a costly source of warranty claims made against vehicle manufacturers. Vibration caused by tire/wheel assemblies tends to be most objectionable at "highway" speeds, that is, speeds in the general range of speed limits and customary vehicle speeds on major highways. A number of reasons have been postulated as contributing to this phenomenon.
First, at speeds lower than highway speeds, tire/wheel induced vehicle vibration tends to be masked by vibrations induced by secondary roadways which are often rougher than highways. Also, at these lower speeds, the vehicle occupants tend to be preoccupied with other sensory inputs, such as linear and angular vehicle acceleration and deceleration.
Another possible reason relates to the structural dynamics of automobiles. Automobiles can exhibit a secondary resonance in the vertical direction in the range of frequencies excited by once per revolution inputs of tires rotating at highway speeds. This secondary resonance and accompanying vertical vibration mode are attributable to the unsprung mass of the vehicle (tires, wheels, and the unsprung portion of the suspension and drive train) acting upon the "spring" represented by the radial spring rate of the tires. Human sensitivity to vibration also appears to be acute in this same frequency range.
Two significant sources of tire/wheel assembly induced vibration in the plane perpendicular to the axis of rotation of the assembly are static imbalance and radial force variation. Sources of induced vibration induced by tire/wheel assemblies can be broadly classified into two categories; those which vary as a function of the rotational speed of the assembly and those which are substantially independent of speed. Static imbalance induces vibration in both the vertical (i.e. radial) and horizontal (i.e. fore/aft) directions in a manner which increases dramatically with speed. In contrast, radial force variation acts only in the vertical direction and has been observed to be substantially independent of speed. Vertical vibration, whether due to static imbalance, radial force variation or a combination of the two, tends to be sensed by the occupants of a vehicle primarily through the vehicle body. On the other hand, the horizontal vibration caused by static imbalance tends to be transmitted through the steering mechanism and sensed by the driver of a vehicle at the steering wheel.
Because of these significant differences in behavior, conventional practice in mitigating vibration has most commonly been to address static imbalance and radial force variation as being separate and distinct from one another. Being substantially independent of speed, radial force variation has been addressed other than by altering static imbalance which produces forces which change with speed. Likewise, tire/wheel assemblies have been traditionally balanced so as to exhibit substantially zero net static imbalance irrespective of their force variation characteristics. Before describing these conventional practices, it is appropriate to consider the nature of static imbalance and radial force variation as well as the manner in which they are measured.
Static imbalance in a tire/wheel assembly results from an uneven distribution of mass around its axis of rotation and can be defined as a vector directed from the axis of rotation toward the center of gravity of the assembly. The magnitude of that vector is given by the product of the mass of the tire/wheel assembly and the distance by which its center of gravity is offset from its axis of rotation. When the assembly rotates, static imbalance produces a centrifugal imbalance force of a magnitude equal to the product of the imbalance and the square of the angular velocity at which the assembly rotates. It is for that reason that the magnitude of vibration caused by a given amount of imbalance varies as a function of speed. Due to the continuously acting, rotational nature of centrifugal force, static imbalance tends to induce vibration in the fore/aft direction as well as in the vertical direction. Because the magnitude of this centrifugal force varies according to the square of the angular speed of the tire/wheel assembly, the vibration transmitted through the vehicle body as well as that sensed at the steering wheel becomes more noisome as vehicle speed increases.
Static imbalance of tire/wheel assemblies can be measured on any of a number of types of available equipment including the familiar static or dynamic balance machines, such as those commonly used in automotive shops. In a typical static balance machine, a tire/wheel assembly is mounted upon a pivotable spindle. Gravity causes the center of gravity of the assembly to align vertically with the pivot point. A bubble indicator responsive to the direction and degree of pivoting of the spindle is then read to determine the static imbalance. The tire/wheel assembly is not rotated during this procedure.
A typical dynamic balance machine operates by mounting a tire/wheel assembly on a spindle and then rotating the assembly about the spindle axis. Since the assembly will attempt to rotate about its center of gravity irrespective of the original position of the spindle, static imbalance can be determined by resolving the forces tending to move the spindle as the tire/wheel assembly rotates. Some dynamic balance machines are capable of simultaneously measuring static imbalance and another type of imbalance known as "dynamic imbalance" or "couple" which indicates the tendency of a tire/wheel assembly to tilt from side to side as it rotates. Couple is undesirable since it represents a source of vibration which is independent of static imbalance.
Prior art attempts to reduce, vibration generated by static imbalance have typically sought to produce a tire/wheel assembly whose static imbalance was as close to zero as practicable so that the assembly would generate substantially zero imbalance force when rotating. This was done by first measuring the imbalance initially present and then attempting to cancel that measured imbalance by adding to the assembly an equal and opposite compensating imbalance. Such compensating imbalance was applied by mounting one or more weights to the assembly at a location 180.degree. opposite from its center of gravity in the rotational plane so as to oppose the measured imbalance. In order to null static imbalance, the weight was typically mounted on the wheel and was selected such that its mass multiplied by the radial distance between the weight and the axis of rotation would generate a countering static imbalance equal and opposite to the measured static imbalance. Thus, in the prior art, both the mass of the applied weight and its mounting orientation were typically selected without regard to force variation.
A similar approach has been taken to reduce vibration generated by dynamic imbalance. The dynamic imbalance initially present in a tire/wheel assembly is measured (usually while simultaneously measuring static imbalance) and then nulled by applying weights or otherwise altering the mass of the assembly. In order to correct for dynamic imbalance it is generally necessary to alter the mass of a tire in each of two planes, one of which is located on the "inner" or "vehicle" side of the assembly and the other of which is located on the "outer" or "curb" side of the assembly. These inner and outer planes are each perpendicular to the intended axis of rotation and are mutually spaced apart from one another.
Rather than adding separate sets of weights to null static and dynamic imbalance separately, modern balance machines are capable of measuring both quantities at once and specifying the mass and location of a weight to be added to each respective inner and outer plane in order to null static and dynamic imbalance in a single operation. One such machine which has a high throughput capacity and is intended for use in a tire/wheel production process is the Model ATW-231 available from ITW Micropoise of Indianapolis, Indiana. This machine includes an adjacent weighting station which includes a display for indicating to an operator the weight (or mass) and angle of counterbalance weight to be applied to each respective inner and outer plane at a predetermined correction radius so as to substantially null both static and dynamic imbalance in a single operation.
Radial force variation in a tire/wheel assembly is distinct from imbalance and can be generated by either the tire, the wheel or both. When a tire rotates along a surface under a radial load such as that due to the weight of a vehicle, structural nonuniformities in the tire give rise to self-excited fluctuations in the reaction forces exerted between the tire and the surface along various directions. The fluctuations of these forces in the vertical direction represent radial force variations generated by the tire.
Radial force variation, as well as other parameters indicative of tire nonuniformity, is measured using a uniformity machine. In a typical uniformity machine, an inflated tire is rotatably driven with its tread surface in forced contact with the circumferential surface of a loadwheel. The loadwheel rotates on a spindle which, coupled to a force transducer, measures forces acting on the load-wheel in directions of interest, including the radial direction. A rotary encoder tracks the rotation of the tire by generating a series of equiangularly spaced pulses as the tire rotates. Those pulses, together with signals indicative of the instantaneous forces registered by the force transducer are communicated to a computer associated with the machine. In response to the pulses, the computer samples and stores a series of measurements of the force-indicating signals over a complete revolution of the tire. The computer then carries out a Fourier analysis to determine at least one nonuniformity-indicating parameter based on one or more selected harmonics of the force-indicating signal. Each harmonic is conventionally represented in vector form as a magnitude and an angle, the latter of which corresponds to a particular angular location on the tire. Acceptable tires are usually marked on their sidewall to indicate the angular location at which a selected harmonic of radial force variation, typically the first order harmonic, reaches its peak value. The tire is graded by comparing the measured value of one or more nonuniformity indicating parameters to previously determined specification criteria. Such criteria are usually specified as numerical limits indicating that the tire should either be rejected, accepted or subjected to corrective measures in attempt to bring its performance within acceptable limits.
It is known for example to correct for excessive radial force variation by removing material from selected portions of the tire tread. This is commonly carried out by providing a tire uniformity machine with one or more selectively actuatable grinders operating as disclosed for example in Rogers et al. U.S. Pat. No. 4,458,451 which is expressly incorporated herein by reference in its entirety. While often beneficial, such techniques do not guarantee acceptably low levels of radial force variation in tire/wheel assemblies. One reason for this is that, as noted previously, tires are not the only potential contributors to radial force variation in tire/wheel assemblies. As the assembly rotates, dimensional nonuniformities in the wheel can also induce radial force variation.
Dimensional nonuniformities in wheels such as radial runout at the bead seat of a wheel, can cause radial force variation in a tire/wheel assembly by interacting with the radial spring rate of the tire. For example, assume that a given wheel has an average radial runout of x (inches) at a particular angular location on its beadseat and further assume that a tire having an effective radial spring rate of k (pounds per inch) is mounted upon that wheel. Such runout can be expected to contribute a radial force of k times x (pounds) when that angular location aligns with the vertical axis. In a tire/wheel assembly, any radial force variation contributed by dimensional nonuniformities in the wheel combine with that contributed by the tire to produce a resultant radial force variation which indicates the tendency of the tire/wheel assembly as a whole to vibrate radially. That resultant radial force variation (or harmonics thereof) can be estimated by measuring the radial force variation (or harmonics thereof) generated by the tire and vectorially adding thereto the expected radial force variation expected to be contributed by the wheel based on a separate measurement of the average radial runout of the wheel (or corresponding harmonics thereof).
Vehicle wheels are inspected for dimensional nonuniformity using wheel uniformity analyzers such as the Model SST-WUA wheel uniformity analyzer manufactured by Akron Standard, an ITW Company, located in Akron, Ohio. Such equipment can be used to identify a specific location on the circumference of the wheel, such as the circumferential location 180.degree. opposite the location corresponding to the angle of the first harmonic of the average radial runout of the beadseat of the wheel.
It has been known to attempt to minimize vertical vibration of tire/wheel assemblies by orienting the tire with respect to the wheel such that the vector describing the first harmonic of the radial force variation of the tire is opposed by the vector describing the first harmonic of the average radial runout of the wheel. When the tire and wheel making up an assembly are so oriented, the first harmonic of radial force variation of the tire tends to be at least partially cancelled by the force component induced by the first harmonic of the radial runout of the wheel and vice versa. This reduces the tendency of the tire/wheel assembly to vibrate in the vertical direction.
A novel method for pairing tires from a given population of tires with wheels from a given population of wheels so as to optimally reduce radial force variation in the resulting population of tire/wheel assemblies is disclosed in copending, commonly assigned U.S. patent application Ser. No. 07/556,951 entitled "Process and Apparatus for Pairing Tires and Wheels" which is expressly incorporated herein by reference in its entirety. However, even such orientation and pairing do not guarantee exact cancellation; some residual radial force variation can be expected to remain in tire/wheel assemblies made from tires and wheels so oriented and paired.